Multi-pole lump solutions and anomalous scattering in the BKP equation

Tianwei Qiu, Zhen Wang and Xiangyu Yang

Chaos, Solitons & Fractals, 2025, vol. 198, issue C

Abstract: This study investigates the dynamics of multi-pole lump solutions and their scattering phenomena in the Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation. Utilizing the inverse scattering transform method, we generate standard M-lump solutions from eigenfunctions with simple poles and derive non-standard lump solutions associated with higher-order poles in their eigenfunctions. While standard M-lump waves exhibit normal scattering phenomena, multi-pole lump waves display time-dependent velocities and non-trivial scattering angles, referred to as anomalous scattering. Notably, this research introduces a novel triple-pole lump solution in the BKP equation. These anomalous scattering phenomena differ from those observed in the Kadomtsev–Petviashvili equation but exhibit similarities to those in the Davey–Stewartson system.

Keywords: Lax pair; Discrete spectrum; Multi-pole solution; Anomalous scattering; BKP equation (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:198:y:2025:i:c:s0960077925005351

DOI: 10.1016/j.chaos.2025.116522

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